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Fisher, Q, Lorinczi, P, Grattoni, C orcid.org/0000-0003-4418-2435 et al. (5 more authors) (2017) Laboratory characterization of the porosity and permeability of gas shales using thecrushed shale method: Insights from experiments and numerical modelling. Marine and Petroleum Geology, 86. pp. 95-110. ISSN 0264-8172

https://doi.org/10.1016/j.marpetgeo.2017.05.027

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Accepted Manuscript

Laboratory characterization of the porosity and permeability of gas shales using thecrushed shale method: Insights from experiments and numerical modelling

Quentin Fisher, Piroska Lorinczi, Carlos Grattoni, Konstantin Rybalcenko, Anthony J.Crook, Samuel Allshorn, Alan D. Burns, Ida Shafagh

PII: S0264-8172(17)30186-1

DOI: 10.1016/j.marpetgeo.2017.05.027

Reference: JMPG 2920

To appear in: Marine and Petroleum Geology

Received Date: 16 January 2017

Revised Date: 17 May 2017

Accepted Date: 18 May 2017

Please cite this article as: Fisher, Q., Lorinczi, P., Grattoni, C., Rybalcenko, K., Crook, A.J., Allshorn, S.,Burns, A.D., Shafagh, I., Laboratory characterization of the porosity and permeability of gas shales usingthe crushed shale method: Insights from experiments and numerical modelling, Marine and PetroleumGeology (2017), doi: 10.1016/j.marpetgeo.2017.05.027.

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Laboratory characterization of the porosity and permeability of gas

shales using the crushed shale method: Insights from experiments

and numerical modelling

Quentin Fisher1, Piroska Lorinczi1, Carlos Grattoni1, Konstantin Rybalcenko1, Anthony J. Crook2, Samuel Allshorn1, Alan D. Burns1 and Ida Shafagh3 1School of Earth and Environment, University of Leeds, Leeds, LS2 9JT, UK

2 Three Cliffs Geomechanical Analysis Ltd, Roseleigh, Swansea, SA3 2EN, UK

3School of Civil Engineering, University of Leeds, Leeds, LS2 9JT, UK

Abstract

Gas production from shale resource plays has transformed the USA energy market. Despite

the knowledge gained from the analysis of large amounts of shale core, appraisal of shale

gas resource plays requires a large number of wells to be drilled and tested. Ideally, core

analysis results would provide an indication of both the gas filled porosity and permeability of

shale resource plays, which could then be used to reduce the number of wells needed

during appraisal. A combination of laboratory experiments, numerical modelling and a round-

robin test have been conducted to assess the validity of the crushed shale method (CSM),

which has been widely used in industry to assess the porosity and permeability of shale. The

results suggest that the CSM can provide reasonably precise estimates of porosity

measured at ambient stress if a standard sample cleaning method is adopted; although a

reliable method to correct these values to subsurface conditions needs to be developed. The

CSM does not, however, appear to provide useful information on shale permeability. A

round-robin test shows that differences of up to four orders of magnitude in permeability

were provided by different laboratories when analysing the same sample. These huge

differences seem to occur due to a combination of errors in calculating permeabilities from

pressure transients, differences in the way that permeability is calculated as well as

uncertainties regarding the effective size of crushed shale particles. However, even if

standardized, the CSM may not be particularly useful for characterizing the flow capacity of

shale because it is insensitive to the presence of high permeability zones that would control

flow in the subsurface.

Keywords: shale gas, permeability, porosity, crushed shale method, pressure transient

analysis

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Introduction

Shale gas production has revolutionized the energy market in the USA where production

reached 40 bcf/d in 2015 and contributed around 50% of the total dry gas produced (IEA,

2015). By 2014, over 50,000 producing wells had been completed in the seven key shale

gas plays, Barnett, Haynesville, Woodford, Fayetteville, Marcellus, Eagle Ford, and Bakken

(Hughes, 2015). Exploration and appraisal of shale gas resource plays is now active in many

other parts of the world including: Australia, Argentina, China, India, Mexico, Poland,

Romania and the UK. Appraisal of shale gas resource plays remains difficult and expensive

despite the large number of wells that have been drilled, cored and tested. For example,

Haskett (2014) suggested that over ten pilot wells may be needed to have 90% confidence

that the results are representative of the shale gas play. Also, up to 100 wells may be

needed before optimal production efficiency has been reached and production costs

minimized (Haskett, 2014).

Appraisal of shale gas resource plays differs significantly from that of conventional

reservoirs. In particular, appraisal of conventional reservoirs often involves drilling, coring

and testing a small number of wells and then building geological and simulation models

based on core analysis data to predict the volume of petroleum present and future

production rates as well as to optimize production strategies. Appraisal of shale gas

resource plays involves the drilling and testing of far more pilot wells with less emphasis on

core analysis and little or no emphasis on production simulation modelling.

The reduced emphasis on core analysis and production simulation modelling in shale gas

resource plays is a response to several realities. First, there remains a large uncertainty

regarding how gas flows from the shale matrix to hydraulic fractures. For example, the role

of natural fractures, sedimentary lamina with higher permeability, and the presence of

intragranular vs. organic matter porosity in controlling gas storage and flow rates are still

widely debated (e.g. Schieber, 2010; Curtis et al., 2012). Second, shale gas resource plays

are heterogeneous in terms of their sedimentology, gas distribution, fracture content and

stress magnitude/orientation so many wells are needed to estimate average performance.

Third, there are no well-established links between core analysis results and production rates.

Indeed, despite a large number of core analysis measurements being conducted, there

exists little consensus on how they can be used to estimate flow rates. Forth, industry-

standard protocols for the analysis of shale core do not exist. Indeed, comparative studies,

often referred to as round-robin tests, indicate laboratories provide very different

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measurements of key properties, such as porosity and permeability (Passey et al., 2010;

Dadmohammadi et al., 2016).

The current paper addresses key issues regarding the analysis of cores obtained from shale

gas resource plays. In particular, it attempts to critically appraise the meaning of results from

the laboratory method most commonly used by industry to assess the porosity and

permeability of shale samples – namely the crushed shale method. In doing so, it attempts to

identify causes of discrepancies between laboratories and provide recommendations for

future core analysis. The paper begins by providing a review of the laboratory techniques

that are commonly used to assess the porosity and permeability of core samples from shale

gas resource plays. Results from numerical modelling and laboratory analysis are then used

to provide some insight into the meaning of porosity and permeability data obtained from

shales. The laboratory experiments conducted by the authors of this paper have been

combined with a round-robin test in which the porosity and permeability of six shale samples

have been analyzed by three of the leading companies providing shale analysis services to

industry.

Laboratory characterization of the storage and flow capacity of gas shale

Porosity and permeability analysis of conventional reservoirs

To place the analysis of gas shale into context, the methods that are commonly used to

measure storage and flow capacity of conventional reservoirs are briefly described. Porosity

is the primary measure of the total storage capacity of gases and liquids in conventional

petroleum reservoirs. Permeability is used as the main measure of the flow potential of

conventional reservoirs. Porosity and permeability are usually measured on 1 or 1.5 inch

diameter core plugs, which have been cleaned and dried to remove brine, hydrocarbons and

drilling fluids.

The porosity of conventional reservoirs is defined as the pore volume divided by bulk

volume. Pore volume is generally not measured directly. Instead, porosity is calculated from

measurements of bulk, ρB, and grain, ρG, density using:-

∅ = 1 − ���� (1) Mercury immersion has long-time been considered the gold standard for bulk density

analysis although laser scanning is increasingly being used so as to reduce the use of toxic

mercury. Grain density is usually determined using helium pycnometry. Bulk density is

normally measured at ambient stress conditions so pore volume compressibility corrections

need to be applied to extrapolate porosity measurements to in situ conditions.

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Permeability of conventional petroleum reservoirs is generally measured using steady-state

gas permeametry. In such tests, core plugs are placed in a core holder and confined at a

pressure of ~500 psi. Gas flow is initiated through the sample until steady-state is achieved

and then permeability, k, is calculated using an adaptation of Darcy’s Law, which takes into

account the variable gas density across the sample:-

� = � ��(��� − ���)(2)

where Q is flow rate, µ is viscosity, P1 and P2 are the upstream and downstream gas

pressures at steady-state, A and L are the cross sectional area and length of the core.

Gas slippage enhances flow rates in low permeability sandstones so a Klinkenberg

correction is often applied to the measurements to obtain what is often referred to as the

absolute or liquid permeability, k∞. The best practise is to measure the gas permeability at

several different pressures and then calculate k∞ by extrapolating plots of apparent

permeability (i.e. the measured permeability value without a slip correction) against the

reciprocal of the average pressure, P, to 1/P = 0. Laboratory measurements of permeability

of tight rocks are often very stress sensitive so an overburden correction is often applied to

estimate in situ permeability values.

Laboratory analysis of shale samples

Laboratory analysis of the storage and flow capacity of shale samples is far more complex

than for conventional reservoirs for both practical and theoretical reasons. The first practical

difficulty is that it is generally far more difficult to obtain high quality core plugs from shale

than it is for conventional reservoir rocks. This difficulty can be caused by shales

delaminating as core plugs are taken or as a result of the damage that occurs during coring

and core retrieval. The low permeability of shale means that gas pressure does not easily

equilibrate via natural matrix or fracture porosity as the core is brought to the surface. In

such cases, it expands to create microfractures along which it flows to reach pressure

equilibrium (Zubizarreta et al., 2011, 2013; Ashena et al., 2016). The low permeability of

shale samples means that core plugs are very difficult to clean. Also traditional porosity and

permeability measurements are very time-consuming, which makes the results very

susceptible to leaks from the experimental apparatus. The inability to obtain high quality core

plugs also means that it is often very difficult to measure the pore volume compressibility of

shale, which is needed to estimate porosity at in situ conditions.

There are several issues that impact the measurement of the storage capacity of shales,

which are related to pore size and composition. For example, much of the pore-space in

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shale is on the nm-scale so may be less accessible to methane than to helium. So the grain

volume measured using helium could be lower than measured using methane. However,

methane adsorption may lead to the swelling of organic matter, which would mean that pore

volume could be overestimated when measured using helium compared to the natural

situation where methane is present.

Measuring the gas flow capacity of shales has many of the same issues as for porosity but is

also faced with the additional issue that unlike conventional gas reservoirs, where the

principle flow mechanism is continuum (i.e. Darcy) flow, gas flow in shales may be

dominated by other mechanisms such as slippage, transitional flow or Knudsen diffusion

(Freeman et al., 2011). Gas flow mechanisms depend on the Knudsen number, which is the

ratio of mean free path of the gas molecules to a characteristic length scale; the latter is

generally assumed to be equivalent to the pore-size. The mean free path of gas molecules is

strongly dependent on pressure-temperature conditions, which means that gas flow

mechanisms in the laboratory may differ to those in the subsurface.

New laboratory methods and numerical models for measuring gas flow in shale have been

developed that attempt to address some of these difficulties. Transient pressure techniques

are often used to increase the speed of measuring permeability on core plugs. For example,

Brace et al. (1968) developed the pulse decay permeametry, PDP, which is often used to

measure shale permeability. The PDP test involves applying a pressure pulse to one end of

the sample and recording the response in a downstream reference volume. The pressure

transient is then used (i.e. inverted) to calculate permeability. Improvements in the model

used to invert the pressure transient data have been developed by several groups (e.g. Lin,

1977; Hsieh et al. 1981; Neuzil et al. 1981; Dicker and Smits, 1988).

Numerical models have also been developed to allow the results from pressure transient

tests to take into account gas flow mechanisms other than continuum flow (i.e. gas slippage

and Knudsen diffusion) as well as gas adsorption on organic matter (e.g. Cui et al., 2009;

Civan et al., 2011a,b). Linking these models to inversion algorithms provides the theoretical

framework to obtain the key parameters that control gas flow in shale from the transient

experiments. However, it has been argued that these models may contain too many

unknowns, of which several are too closely correlated, to allow their use in the day-to-day

analysis of shale (Lorinczi et al., 2014).

Although these developments go some way to increase the speed of sample analysis and

take into account potentially important processes affecting gas flow in shale, they do not

address other key issues such as the difficulty in obtaining and then cleaning undamaged

shale core plugs. So a far more radical solution was proposed by workers at the Gas

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Research Institute (Luffel and Guidry, 1992; Luffel et al., 1992; Luffel, 1993; Luffel et al.,

1993) to address these issues. The method proposed, commonly referred to as the GRI or

crushed shale method, CSM, involves conducting transient pressure experiments on

crushed shale using an experimental set up similar to that illustrated in Figure 1. Crushed

shale is placed into a sample chamber into which helium gas is expanded from a reference

chamber at a known initial pressure. The pressure rapidly drops to a value dictated by the

dead space in the sample cell, then it decays more slowly to a lower pressure as the gas

moves into the pores within the crushed shale particles. Material balance is then used to

calculate the grain volume and analytical or numerical methods are used to invert the

pressure transient to calculate an apparent permeability. Bulk density is usually measured

separately using mercury immersion. However, it has also been suggested that it is possible

to extrapolate the pressure vs time, t, data to t0.5 = 0 and then apply material balance to

calculate the bulk volume of the crushed shale (Luffel et al., 1992). The combination of grain

volume and bulk volume can then be used to calculate porosity in a single measurement.

Figure 1 Schematic diagram of a pressure pulsed-decay test of a crushed sample (after Profice et al., 2011).

Luffel (1993) argued that the CSM had several advantages over the core plug based

techniques including:-

• The high surface area to volume ratio of the crushed shale fragments means that the

test can be conducted in a few minutes rather than the hours to days needed for the

transient experiments on core plugs.

• The crushed shale particles are sufficiently small that they can be cleaned prior to

analysis.

• The shale fragments along microfractures resulting in particles that are undamaged

so the results could be treated as being true matrix properties.

These arguments have led to the CSM becoming widely used by the shale gas industry as

the preferred method for measuring porosity and permeability. However, despite its

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widespread use, many concerns have been raised regarding the validity of the CSM. For

example, round-robin tests have shown that considerable differences in results are provided

by different laboratories when the same shale sample was provided for analysis. In

particular, Passey et al. (2010) report 100% differences in porosity and four orders of

magnitude in permeability in the results provided by three leading service companies

analysing the same samples. Several studies have suggested that the differences in porosity

was due to the sample cleaning procedures used by the laboratories (Handwerger et al.,

2011; Lalanne et al., 2014). In particular, one laboratory used the retort method to remove

water and moveable hydrocarbons whereas the others used a solvent extraction technique

followed by an extended period of drying (often in excess of a week) in a vacuum oven at

110oC.

Causes for the differences in permeability results have not been as widely investigated,

which is partly because service companies tend not to disclose the exact details of the

sample analysis workflows, data inversion methods or even the raw pressure data collected

during the experiments. Several theoretical arguments have, however, been raised about the

validity of the CSM. A particularly important criticism is that interpretations of CSM results

generally assume that Darcy flow is the main gas flow mechanism and ignore other gas flow

mechanisms (Civan et al., 2015).

The models used to interpret CSM measurements range considerably in sophistication. The

original work conducted by the Gas Research Institute used a simulation model to calculate

permeability from pressure transients (Luffel et al., 1992). The simulation model assumed

the shale fragments had a barrel shape, gas was not adsorbed to the constituents of the

shale and that continuum flow was the dominant gas flow mechanism. Profice et al. (2011)

provide an analytical solution for gas flowing into spherical shale particles, which also

applies the Klinkenberg b-factor to take into account gas slippage. However, Profice et al.

(2011) concluded that it was generally not possibly to accurately invert for both an absolute

permeability and the Klinkenberg slip coefficient from a single measurement. Cui et al.

(2009) also developed analytical solutions for gas flow into shale samples, which take into

account gas adsorption on organic matter. Civan and Devegowda (2015) presented a

sophisticated model for gas flow into shale particles, which takes account of gas adsorption

as well as the key gas flow mechanisms. The model is solved numerically and combined

with an inversion code that theoretically allows the key parameters controlling gas flow in

shale to be inverted from CSM data. Mathur et al. (2016) described a sophisticated gas flow

permeameter capable of conducting steady-state and transient permeability measurements

on core plugs. The permeameter was used to conduct steady-state and transient gas

permeabilities using helium and nitrogen at gas pressures ranging from 100 to 3200 psi

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maintaining a net effective confining pressure of 3000 psi. The results from the experiments

were within 30% of each other when a double slip correction was applied indicating that low

pressure measurements are dominated by transitional flow. Dadmohammadi et al. (2016)

described how the pressure step decay method could be used to make reproducible

estimates of the permeability, porosity, pore volume compressibility and Klinkenberg b-value

of ultralow permeability (~40 nD) pyrophyllite samples.

The effect of the shale particle size used in the CSM has been investigated by several

authors (e.g. Cui et al., 2009; Profice et al., 2012; Tinni et al., 2012; Civan and Devegowda,

2015). In general, these studies have shown that the measured permeability increases as

the size of the crushed shale fragments increases. For example, Tinni et al. (2012) found

that permeability values can change by over two orders of magnitude when the size of the

particle varies between 0.7mm and 7mm. Profice et al. (2012) suggested that a particle size

should be used that is specifically selected to guarantee a reliable pressure decay recording.

Using shale fragments that are too small results in a relaxation time that is too fast to be

interpreted.

Another criticism of the CSM regards its inability to perform measurements at reservoir

stress conditions or measure how permeability is likely to change during production (Heller

et al., 2014). To tackle these flaws, Heller et al. (2014) carried out a series of laboratory

experiments to investigate the effects of confining stress and pore pressure on permeability

during production from gas shale reservoirs.

Experimental methods

A round-robin test has been conducted to better understand the reasons for the

discrepancies between different laboratories using the CSM. Six 10-15 cm long, 10 cm

diameter cores, here referred to as samples SH1-6, were cut perpendicular to bedding to

obtain four identical subsamples. The samples were chosen because they appeared

homogenous during visual inspection and from the analysis of CT scans generated from a

medical-type CT scanner. Three of these subsamples were sent to different core analysis

laboratories, here referred to as LabA, LabB and LabC, to have their porosity, permeability,

grain density and bulk density analysed using the CSM. In addition, the laboratories were

asked to take core plugs of the samples and measure permeability using the pulse-decay

method. The forth subsample went through a very extensive sample analysis and

characterization program at the University of Leeds. The analyses conducted at the various

laboratories are described below.

Analysis conducted at the University of Leeds

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The analysis conducted by the authors of this paper included a detailed sample

characterization program as well as transient gas flow tests on both crushed shale and core

plugs. The basic sample characterization program included:-

• Microstructural examination using scanning electron microscopy on samples polished

using a broad ion beam polisher. These measurements were made on both polished

thin sections made from both crushed and uncrushed core material.

• Mineralogical analysis using quantitative X-ray diffraction (QXTD)

• Major element analysis using X-ray fluorescence (XRF)

• Organic and inorganic carbon using an elemental analyser

• Surface area analysis using the BET method

• RockEval pyrolysis

• Hg-injection analysis was conducted on 1cm3 shale samples using a Micromeritics

Auto Pore IV porosimeter.

• Bulk density using mercury immersion

• Thermogravimetric analysis

A section of the core was then taken and crushed using an agate pestle and mortar. The

crushed shale was sieved and the 20/35 mesh fraction (500 to 840 µm) retained for analysis

using the CSM. This fraction was then divided into two subsamples. The first was treated as

“as received” and analysed using the CSM. The second was weighed, oven dried at 110oC

for 7 days and then reweighed to determine the amount of liquid lost during drying. The

samples were immediately placed in a desiccator prior to CSM analysis, which was

conducted using a similar apparatus to that shown in Figure 1. The instrument used has

reference and sample chamber volumes of 40.1 and 73.3 cm3 respectively. Typical sample

volumes of 25 to 35 cm3 were used in the experiments. Helium gas at a pressure of 150-200

psig was expanded into the reference volume and allowed to reach temperature equilibrium

before being expanded into sample chamber, which was typically at atmospheric pressure.

Tests were conducted to assess whether varying the initial pressure between 150 and 200

psi significantly impacted the results but this proved not to be the case. Tests were also

conducted to assess whether the results were improved by pre-flushing the cell with helium

or placed under vacuum prior to analysis but no significant difference was identified. The

pressure transient was recorded using a Mensor transducer at a rate of one measurement

every 0.04s for around 2000s. Boyle’s Law was used to determine the grain volume. Bulk

volume was estimated from the weight of the sample and its bulk density. The latter was

determined from mercury immersion measurements conducted on core plugs that were

corrected for the weight loss that occurred during sample drying. The pressure transient was

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used to calculate an apparent permeability using analytical and numerical methods

described below (i.e. the permeability calculated was not Klinkenberg corrected).

Core plugs from the sample were also analysed using a pulse decay permeameter similar to

that described by Jones (1997). The samples were confined at around 3000 psi and helium

at a pressure of around 1000 psi was used as the permeant. The results from the

experiment were inverted numerically using a dual porosity model in which a discrete

fracture was incorporated into the model. The results from these experiments are included

for completeness and will be described in more detail in a future publication.

Analysis conducted in LabA

Samples were analysed in this laboratory using virtually the same method as developed by

GRI (Luffel et al., 1993). Each sample was weighed to ± 0.001 g and the bulk volume

measured by Hg-immersion to ± 0.01 cm3. A core plug was then drilled from each sample

perpendicular to the lamination. The remaining sample was crushed with a mechanical rock

crusher and sieved to obtain the 20/35 US mesh fraction. These steps were performed as

quickly as possible to limit evaporation of fluids from the sample. The 20/35 fraction was

then sealed in air tight vials and divided into two subsamples. Porosity and permeability of

one subsample was measured using the GRI method. The second subsample was

transferred to a Dean Stark apparatus and refluxed in toluene for 7 days. Fluid volumes were

checked twice a day to ensure complete water extraction. The samples were then dried for

at least a week at 110oC and until weight stabilization (i.e. ± 0.001 g) was achieved. The

samples were then transferred to a desiccator where they were kept until the porosity and

permeability was measured using the same procedure as described by Luffel et al. (1993).

The permeability measurements were made using helium gas at around 200 psig. Pressure

measurements were made at 0.25 s intervals for a maximum of 2000 s. Oil and gas volumes

were calculated from the results of the Dean Stark analysis assuming densities of 0.8 and

1.018 g/cm3 respectively. The permeability of core plugs were measured using the PDP

technique described by Jones (1997) at a helium pressure of 1000 psi and confining

pressure of 5000 psi.

Analysis conducted in LabB

A core plug was then drilled from each sample perpendicular to the lamination. Bulk volume

and bulk density were measured on the bulk sample as received although the exact method

used was not disclosed by the laboratory. The sample remained after the core plug was

taken was crushed and divided into two subsamples; no details were provided regarding the

size of the shale fraction used. One subsample was treated as “as received” and analyzed

using a proprietary version of the CSM. The numerical method used to calculate the

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permeability from the pressure transient was not provided. The second subsample was used

to measure the moveable oil, the total water content, the structural water and clay bound

water using the retort method. The sample was then used to measure the dry grain density,

porosity and permeability using a proprietary version of the CSM. No details were provided

regarding how the samples were stored after drying. The core plug was analysed using a

PDP technique but no information was provided regarding the instrument used or the

algorithm used to calculate the permeability. Measurements on the core plug were made

using a gas pressure of around 1000 psi and net confining pressures of 500, 1500, 3000 and

5000 psi.

Analysis conducted in LabC

Bulk volume and bulk density were measured on the bulk sample as received although the

exact method used was not disclosed. A core plug was then drilled from each sample

perpendicular to the lamination. The remaining sample was then crushed into particles of

<1/8 in diameter before being divided into two subsamples. One subsample was treated as

“as received” and the porosity and permeability measured using a propriety version of the

CSM. The numerical method used to calculate the permeability from the pressure transient

was not revealed. The second subsample was dried in a vacuum oven at 100oC for an

unspecified time and then analyzed using their propriety version of the CSM. No details were

provided regarding how the samples were stored after drying. The core plugs were analysed

using a PDP technique but no information was provided regarding the instrument used or the

algorithm used to calculate the permeability.

Numerical modelling of gas flow in shale

A range of analytical and numerical models were used to both invert the pressure transient

results obtained from the crushed shale experiments and also to explore key controls on the

experiments; these are described below.

Analytical models

The analytical models presented by Profice et al. (2011) and Cui et al. (2009) were used to

invert the pressure transient data obtained from the crushed shale experiments. The model

of Profice et al. (2011) combined the mass conservation with the momentum conservation

(Darcy-Klinkenberg) equations to give the following analytical solution:

��(�) =����� 3��3����� + ��� +

2��

��!∀# ∃−%&����� �∋ sin(%&)��+��%& cos(%&) + (�� + 2��) sin(%&).&+ ��/�

01112��

,(3)

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where

� = ����4��/� − ��/�5,(4)

� = �(7� + 87)9:;<� (5) and

� = �>�9: (6) The terms denoted by %& are the roots of the equation:

tan(%&) = %&1 + ��%&���

(7)

Cui et al. (2009) developed an analytical method to calculate shale permeability from

pressure transient obtained during the crushed shale experiment based on the one

dimensional diffusion equation. The approach assumes that gas flow is controlled by Darcy’s

law and that the crushed shale fragments are spherical with a constant size. The method

can also take into account gas sorption. Cui et al. (2009) suggest that the mass fraction, FR,

of gas in the reference cell and dead volume of the sample cell that is eventually

incorporated into the shale can be calculated using:-

ΧD = 1 − (�Ε + 1)(�Ε� − �)�Ε� − �� (8)

where for a non-absorbing gas Kc is the ratio of the dead volume in the experimental

apparatus divided by the pore volume of the shale, Vb is the bulk volume of the shale, ρ0 is

the original gas densities in the reference cell, ρ is the gas density in the reference cell

during the experiment and ρc0 is the initial average gas density in the sample and reference

cells given by:-

�Ε� = �Γ�7Γ + ��(7Η − 7Ι)7ϑ (9)

where ρr0 is the initial gas density in the reference cell. The slope, s1, of the late-time

behaviour of plots of ln(FR) vs t can then be used to calculate permeability using the

equation:-

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� = �Λ�∅�ΜΝΟ�Π�� (10)

where Ra is the radius of the shale fragments, µ is the gas viscosity, cg is the gas

compressibility, and α1 is the first root of the equation:-

tanΠ = 3Π3 + �ΕΠ� (11)

In this analysis, late-time behaviour is defined being for dimensionless time, tD > 0.1, where:-

�Σ = ��∅ΜΝ��Λ� (12)

Cui et al. (2009) also presented an early time solution for the CSM test. This was not used

during the current study because the pressure measurements in the first few seconds of the

gas entering the sample chamber were not stable.

Numerical models

Eclipse 100TM from Schlumberger was used to model gas flow into the shale particles. A

double porosity permeability model with 10 x 10 x 42 grid blocks was constructed with each

grid being a cube of 100µm length. The reference chamber was represented by 10 x 10 x 15

gridblocks. Two separate regions each of 6 x 6 x 8 grid blocks were placed in the centre of

the remainder of the model to represent shale particles; these could be given the same or

different poroperm properties for a single and double porosity model. The remainder of the

cells within the model represented the dead volume in the sample chamber. The grid blocks

representing the dead volume and reference chamber were assumed to have a permeability

of 10 D and their porosity was adjusted so that the ratio of their pore volume to that of the

total volume of shale was identical to the ratio of volumes of the shale to the space within the

dead volume and reference volume. This model was then used to explore the controls on the

GRI results and also to history match the experimental data. EnableTM from Emerson was

used to history match the pressure transient data from the experiments. The software was

set up to conduct 50 scoping runs in which the key unknowns, porosity and permeability,

were randomly varied between the range estimated by the analyst. The software then

employs a neighbourhood algorithm to identify the values which best fit the transient data

using a further 50 refinement runs. The entire pressure transient after the measurements

become stable (i.e. around 2s) is used in the history match procedure so this is equivalent to

the late-time solution of Cui et al. (2009).

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Figure 2 Cross section of the grid used to model the crushed shale experiment. The red and yellow cells represent the reference volume and dead volume respectively whereas the blue cells represent the shale particles. The shale particles can be given the same or different poroperm properties for a single and double porosity model.

Results

Bulk Density

The round-robin test showed that there was a reasonable agreement between the bulk

density calculated by the four laboratories (Figure 3). In particular, standard deviation of bulk

densities were 0.015g/cm3, which is around 0.5%.

Figure 3 Bulk density results from the round-robin experiment.

Grain density

The round-robin test showed that there was a reasonable agreement between the grain

density calculated by the four laboratories (Figure 4). In particular, standard deviation of

grain densities was 0.02g/cm3, which is around 0.8%. It should, however, be noted that LabB

produced results that are around 0.05 g/cm3 lower than the other laboratories. If data from

LabB are removed the results from the other laboratories have a standard deviation of

0.013g/cm3 or 0.5%.

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Figure 4 Grain density results from the round robin experiment.

Porosity

There is a reasonable agreement between the dry porosity obtained by the four laboratories.

In particular, all porosity measurement agree within 0.9 p.u. with an average standard

deviation of 0.67 p.u. (Figure 5). Porosity values produced by LabB are around 0.5 p.u.

lower than the other three laboratories due to the differences in the grain density

measurements. If LabB measurements are neglected the average standard deviation for the

porosity measurements is <0.3 p.u.

Figure 5 Porosity results from the round robin experiment.

Permeability

Crushed shale method

The permeability results obtained by the service companies using the CSM are provided in

Table 1; the raw pressure data was not provided so it was not possible to conduct further

analysis of the results. A far more detailed analysis could be conducted on the data collected

by the authors. In all cases, the pressure in the reference volume rapidly falls and then starts

to rise reaching a maximum at around 1s (Figure 6). The pressure then falls until it reaches

the final equilibrium pressure, Peq. The early time behaviour is always marked by an initial

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rapid fall followed by a rise in pressure. It is tempting to assume that this early behaviour is

caused by the cooling of the gas as a result of expansion. However, helium is not affected by

the Joule-Thompson effect in this way at these pressure and temperature conditions.

Instead, the instability of the early time data is possibly caused by the gas compressibility,

flow through pipes and its expansion within the shale particles and the sample chamber.

Multi-expansion tests were performed to assess whether these would result in increased

pressure stability in this early time region but this proved not to be the case. Therefore, data

collected during the first 2 seconds cannot be used to calculate permeability. Another feature

of the results, which is important to the later discussion, is that P0i, calculated by

incorporating the initial pressures, cell and sample volumes into Boyles Law, is generally far

higher than the initial pressure calculated by extrapolating P vs. t0.5 to t0.5 = 0 (Figure 7). It

appears that a certain proportion of helium enters the shale fragments along pathways that

are more permeable than the remainder of the shale matrix.

The pressure data collected after two seconds were inverted for permeability using the

analytical and numerical models described above; the results are summarized in Table 2. It

was reasonably easy to estimate permeability using the model of Cui et al. (2009). However,

it was noteworthy that the initial values of FR ranged between 0.95 and 0.01. The low values

indicate that a considerable proportion of the gas had entered the pore space of the shale

fragments within the first two seconds after being expanded into the sample chamber. A

second issue with the model of Cui was that in some cases the permeability calculated

varied significantly depending on exactly which part of the ln(FR) vs. time data were used.

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Figure 6 Example of the pressure vs time behavior for the crushed shale tests.

Figure 7 Plot of pressure against square root of time. P0i is the theoretical pressure of the gas in the dead volume before it has entered the pore space of the shale particles. The pressure calculated by extrapolating the pressure data to t0.5 = 0 is 5.696atm, which is signficantly lower than P0i.

It initially proved difficult to calculate permeability using the Profice model. In particular, the

final pressure calculated by the Profice model was far higher than that calculated from the

ideal gas law (Profice (a) in Figure 8). It was, however, noticed that for all experiments

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incorporating a porosity value that was exactly double that calculated from the Ideal Gas

Law into the model of Profice produced exactly the same final pressure as calculated from

material balance (Profice (b) in Figure 8). The exact reason for this discrepancy has not

been established but it appears most likely to be due to errors in the analytical solution

provided by Profice et al. (2012). The best history match to the experimental data obtained

using the model of Profice et al. (2012) was obtained by incorporating a value of Pi0

calculated by extrapolating P vs t0.5 to t0.5 = 0 into the model (Profice (c) in Figure 8). This is

as opposed to Pi0 calculated from the Ideal Gas Law using the initial volumes of the

reference and sample volumes, the total volume of particles present as well as the initial

pressures in the reference and sample volumes. Estimating Pi0 by extrapolating P vs t0.5 to

t0.5 = 0 takes into account that shale particles appear to contain two pore systems; one which

is accessed by the gas almost instantaneously and the true matrix porosity for which the

model of Profice is used to estimate a permeability. In essence, this is the same as was

achieved by the history match using the double porosity numerical model described below.

The EclipseTM-EnableTM model generally provided very poor history matches when a single

porosity was used to represent the shale particles and the initial pressures, volumes, sample

sizes and porosity calculated from material balance were used as input parameters for the

model (EnableTM (a) in Figure 9). The double porosity-permeability model produced very

good history matches, which were similar to the values obtained using the analytical models

(EnableTM (b) in Figure 9). The history match was generally quite insensitive to the

permeability used in the cells representing high permeability regions within the shale so long

as they were higher than around 1mD. The model results were far more sensitive to the

permeability value used to represent the shale matrix. Good history matches were also

achieved by reducing the initial pressure and shale porosity so that the pore volume that was

rapidly accessed by the helium was treated as part of the dead volume (EnableTM (c) in

Figure 9).

Overall, the permeability results obtained in Leeds averaged over two orders of magnitude

lower than provided by the service companies (Figure 10) and in some cases the difference

exceeded four orders of magnitude. Correlations between the results from the different

laboratories were in general non-existent (Figure 11). However, the permeabilities obtained

using the analytical solutions and the double porosity numerical model were in good

agreement.

Sample LabA LabB LabC

SH1 330 530 34

SH2 440 160 250

SH3 110 46 1600

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SH4 83 160 6

SH5 140 300 26

SH6 160 56 1500

Table 1 Permeability data, in nD, provided by Labs A, B and C using the CSM.

Sample Cui Profice EclipseTM

SH1 1 1 4.8

SH2 4.1 4 7.9

SH3 0.042 0.056 0.03

SH4 0.8 1 0.66

SH5 0.27 0.3 0.09

SH6 0.07 0.1 0.07

Table 2 Permeability results, in nD, determined in Leeds using the CSM. The data have been interpreted using two analytical models (Cui and Profice) as well as a numerical model (EclipseTM). The numerical results are from a dual porosity-permeability model but only the low permeability results are provided as the model was very insensitive to the high permeability results.

Figure 8 Match between the experiment data and various model analytical models based on Profice et al. (2012); Profice (a) is the result obtained when using the porosity obtained by material balance and the initial pressure as input parameters; the permeability value used is the same as for the best fit analytical and simulation models. Profice (b) is similar to Profice (a) but double the porosity is entered into the model; Profice (c) was obtained by adjusting Pi0 to that calculated by extrapolating the experimental P vs t0.5 to t0.5 = 0 and then adjusting porosity and permeability to obtain a history match of the experimental data.

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Figure 9 History match using EclipseTM-EnableTM to model the experimental data. EnableTM (a) is a single porosity model that incorporated the porosity calculated from material balance and the initial pressure used in the experiment; the permeability was chosen to obtain the best fit of the experimental data. EnableTM (b) is a double porosity model in which the porosity and permeability two types of shale fragments were varied to achieve a history match. EnableTM (c) is a single porosity model in which the initial pressure and porosity are calculated so that the high permeability porosity is included as dead volume and the permeability altered to achieve a history match of the experimental data.

Figure 10 Permeability results from the round-robin analysis of shale samples using the CSM; the Leeds permeability quoted here is thought to be that of the matrix (i.e. the low permeability in the dual permeability model).

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Figure 11 Comparison of the results from the round-robin exercise for the crushed shale samples.

Comparison with core plug measurements

For completeness, we have included results from pulse-decay tests conducted on shale core

plugs (Table 3); the details of these tests will be discussed in more detail in a separate

publication and these are merely presented here as a comparison with the crushed shale

results. Overall, there was no clear correlation between the permeabilities obtained from

crushed shale analysis and those measured on the core plugs (Figure 12). There are also

no clear correlations between the permeabilities obtained using PDP between the different

laboratories (Figure 13). In the case of results obtained from the service companies, it could

be argued that the core plugs contained fractures and therefore the permeability values

provided by the service companies did not represent those of the matrix. The PDP

measurements conducted in Leeds were inverted for fracture and matrix permeability but

there was still no correlation with the values obtained using the CSM.

Sample Leeds LabA LabB SH1 124 8370 120

SH2 287 240 680

SH3 70 360 493

SH4 0.44 5.8 294

SH5 0.44 2270 118

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SH6 40 21 1180

Table 3 Permeability data (in nD) obtained in Leeds and provided by two of the service companies; LabC did not manage to drill core plugs to make these measurements.

Figure 12 Comparison of permeability values obtained from the crushed shale and core plug PDP technique.

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Figure 13 Comparison of permeability values obtained from the crushed shale and core plug PDP technique.

Discussion

Porosity

The results from the round-robin test conducted during the current study show far more

agreement between the various laboratories than suggested by Passey et al. (2010). All

laboratories provided very similar results for bulk density. Leeds, LabA and LabC produced

very similar results for grain density (average stdev = 0.015g/cm3) and porosity (stdev = 0.3

p.u.). This precision is quite similar to the accuracy that API suggest is typical for

measurements conducted on conventional sandstones. The largest discrepancy between

laboratories was between the grain densities and hence porosities obtained by LabB and the

other laboratories. Handwerger et al. (2011) suggested that the reason for this discrepancy

could reflect the method used to clean the samples and obtain oil and water saturations. In

particular, Handwerger et al. (2011) argued that the Dean Stark method used by LabA

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removes structurally bound water from clays and therefore results in higher porosities and

grain densities. However, neither Leeds nor LabC cleaned the samples using this method

and produced very similar grain densities to LabA. There is also no correlation between the

difference in grain densities measured by LabB compared to the other laboratories and the

clay content of the samples. This suggests that removal of structurally bound water from clay

is not the reason that LabB produced lower porosities. Instead, the results are consistent

with the interpretation of Lalanne et al. (2014) that LabB do not leave samples for a sufficient

length of time within the retort apparatus to remove capillary bound water.

The similarity in results between Leeds, LabA and LabC is encouraging but it should not be

used as evidence that these values accurately reflect subsurface porosity values. It is well

know that the petrophysical properties of tight rocks are very stress dependent and there is a

considerable amount of evidence that the properties of shale are equally if not more stress

dependent particularly considering the damage that is often done to samples during coring

and core retrieval (e.g. Heller et al., 2014). Indeed, microstructural analysis has shown that

all samples contain microfractures that are very unlikely to exist in the subsurface (Figure

14). A method therefore needs developing to overburden correct bulk density and hence

porosity values. It is relatively straight forward to conduct pore volume compressibility

experiments on samples from conventional reservoirs in which the volume of brine expelled

from the sample is measured as the confining pressure is increased. These experiments are

often difficult to conduct on shale samples due to the difficulty of drilling and then saturating

core plugs.

Figure 14 SEM images showing stress release microfractures (arrows) in a shale sample.

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Permeability

Causes for differences between laboratories

The lack of correlation between the permeability measurements supplied by the different

laboratories using the CSM is consistent with the round-robin test reported by Passey et al.

(2010). Overall, the permeability values obtained by Leeds were several orders of magnitude

lower than those provided by the commercial laboratories. Peng and Loucks (2016)

reinterpreted pressure transient data from a turn-key CSM instrument supplied by one of the

service companies. Their calculations produced permeabilities that were two orders of

magnitude lower than the value produced by the instrument. We have also analysed the

same raw data using the analytical and numerical methods described above and get very

similar results to Peng and Loucks (2016). These results suggest perhaps that the results

from one of the commercial laboratories could be in error due to issues related to the way in

which permeability is calculated.

LabB did not provide enough details to allow us to identify the reason why their permeability

values are far higher than the ones calculated by Leeds. LabC used the entire size range of

<1/8 inch for their crushed shale permeability analysis. Peng and Loucks (2016) have

indicated that there is a scale-dependence on shale permeability such that large samples

have higher permeabilities. Alternatively, it is possible that the higher permeability values

when using larger shale fragments is due to the assumption made regarding the lack of

fractures within the shale particles. For example, Cui et al. (2009) presented data showing

that increasing the size fraction used in the CSM resulted in higher permeability values

(Figure 15). These permeability calculations assumed that the size of the shale particles

was equal to their measured value. However, SEM analysis shows that crushed shale

particles always contain a large density of microfractures (Figure 16). These microfractures

could not exist under the effective stress conditions found in the subsurface and are likely to

have formed either as a result of gas expansion during core retrieval or during the crushing

process. These microfractures would allow easy access of the helium to the matrix porosity,

which would invalidate the assumptions regarding the size of the particles used in algorithms

to calculate permeability from pressure transient data. An end-member situation would be

that crushed shale particles contain so many fractures that their effective particle-size is the

same for the different size fractions and therefore each size fraction would produce the same

pressure transient due to rapid helium flow along the fractures. To test the impact that this

would have on the interpretation of pressure transient tests, an EclipseTM simulation has

been run assuming that the sample has the same particle-size and permeability as the

smallest particle-size shown for sample SH-12 in Figure 15 (i.e. 0.4mm and 2.1 nD). The

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pressure transient obtained from this simulation has then been used to calculate

permeability assuming it was generated by experiments conducted with four other particle-

sizes (0.8 mm, 1.6 mm, 3.2 mm and 6.4 mm). The results (Figure 15) have a remarkably

similar slope to that of the data presented by Cui et al. (2009) and reflect the fact that if the

same pressure transient is interpreted assuming different particle-sizes the calculated

permeability will by necessity increase by the square of the assumed particle size divided by

the particle-size used to calculate the pressure transient In other words, the higher

permeabilities provided by the service companies could be due to the use of larger particles

for the CSM analysis and the assumption that the individual shale particles do not contain

fractures. However, another interpretation would be that the matrix permeabilities are

actually far lower than calculated by the service companies but that the shale particles

contain fractures (Figure 15).

Potentially one of the most striking observations regarding the results produced from the

CSM is that they appear inconsistent with microstructural observations. In particular, we

have access to a large amount of microstructural and petrophysical property data from tight

gas sandstones that have permeabilities of <0.001 mD. Comparison of the microstructure of

sample SH-3 (Figure 17), which the core analysis companies have determined has a

permeability of 0.0001 to 0.001 mD with a tight gas sandstone with a similar permeability

(Figure 18) indicate that the latter have pore sizes that are at least an order of magnitude

larger than shale. These microstructural results are consistent with Hg-injection data (Figure

19) indicating that a shale sample has far smaller pore throats than a tight gas sandstone

sample with similar measured permeability. Overall, it seems likely that this inconsistency is

due to the inability of the CSM to produce reliable and accurate permeability results.

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Figure 15 Diagram to illustrate how the interpretation of CSM results is model dependent. If the same pressure transient shown in a) is produced from five different shale fractions with particle sizes represented by b) (with a minimum particle radius of 0.4 mm and largest of 6.4 mm) the calculated permeability will have a relationship with particle size as shown by the “model” results in c). However, if the particles are full of fractures with the same spacing as the minimum particle size as shown by the red lines in d) then the same pressure transient would be produced as shown in a) by all particles having the same matrix permeability as the smallest particle. The relationship between permeability and particle size is similar for the different size fractions of two crushed shale samples (SH-05, SH-12) presented by Cui et al. (2009). In other words, the relationship between fracture permeability and particle radius identified by Cui et al. (2009) is based on the assumption that individual shale particles do not contain fractures.

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Figure 16 BSEM micrograph of a crushed shale fragment; note the large number of microfractures present (e.g. white arrows).

Figure 17 Photomicrograph of sample SH3, for which the crushed shale analysis conducted by the service companies indicates that it has a permeability of 0.001 to 0.0001 mD. At this scale, pores are too small to be observed.

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Figure 18 Photomicrograph of sample a tight gas sandstone which has a gas permeability of 0.00085 mD. Note the difference in scale to the sample shown in Figure 17 and the fact that macropores (white arrows); and micropores between kaolin platelets (black arrows) can be observed.

Figure 19 Hg injection data from SH-3 and a tight gas sandstone with a gas permeability of 0.00085 mD.

Implications of rapid gas entry into shale fragments

The original GRI report suggested it may be possible extrapolation the pressure vs time data

to t = 0 and then apply Boyle’s Law to calculate the shale volume within the sample chamber

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(Luffel, 1993). Calculations conducted during this study suggest that the theoretical pi0 based

on the weight of the shale fragments and their bulk density is significantly higher than the

pressure estimated by extrapolating pressure to t0.5 = 0. The likely reason for this is that a

significant amount of gas has entered the particles very soon (i.e. <1 s) after the valve

connecting the sample chamber to the reference chamber is opened. The results obtained

during this study cannot be used with certainty to identify the type of pore space into which

this gas flows. It is possible that this pore space was created as a result of damage during

coring, core retrieval or during sample preparation; such porosity has no relevance to

subsurface performance and should be ignored. It is, however, possible that such pore

space represents natural fracture and matrix porosity, which would be present in the

subsurface. Such porosity would be incredibly important to characterize because it may be

providing the highest permeability pathways in the subsurface. However, it is clear that the

CSM cannot be used to measure the permeability of such pathways as they become filled

with gas before temperature equilibrium has been reached within the sample chamber.

EclipseTM simulations were also run to assess the sensitivity of the crushed shale method to

key parameters such as sample permeability. For this sensitivity test, a series of models

were run in which the permeability of the sample was varied between 100nD and 10 pD (10-

12 D) and for porosities of 1% and 10%, as well as for particle sizes of 600 µm and 6 mm. A

model was also run in which 17 layers had a permeability of 0.1 nD and one layer had a

permeability of 100 nD. Figure 20 shows results from simulated crushed shale experiments

on rocks with 0.01 nD to 100 nD. A key observation is that pressure equilibration is

extremely fast (<10 seconds) for samples with a permeability of >10 nD. The first few

seconds of data obtained during these experiments are unreliable, which essentially means

that the experiment is not suitable for analyzing samples with such high permeabilities. A

model was also run containing a thin high permeability zone (could be sedimentary

heterogeneity or fracture) in a 0.1 nD matrix. The results indicate that it would be almost

impossible to identify this high permeability streak from the crushed shale test (Figure 21).

Such higher permeability heterogeneities are likely to control the flow behavior of caprocks

(and shale gas resource plays) but would not be identified using the crushed shale method.

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Figure 20 Plots of the pressure decay vs time for simulated crushed shale experiments. The shale is assumed to have a porosity of 10%, a particle size of 600 µm x 600 µm x 1800 µm and permeabilities between 0.01 nD and 100 nD. Note that the equilibration is reached extremely quickly (<10 seconds) for particles with a permeability of 100 and 10 nD.

Figure 21 Plots of the pressure decay vs time for simulated crushed shale experiments. The shale is assumed to have a porosity of 10%, a particle size of 600 µm x 600 µm x 1800 µm. Results from three models are shown. Two have homogenous permeabilities of 0.1 and 100nD. The third is composed of 0.1 nD shale with a 100 nD high permeability streak making up 5% of the pore volume.

Recommendations for the use of the crushed shale method

The work conducted during the current study has highlighted several key problems when

attempting to use the CSM to estimate the permeability of shale. A huge difference between

the values provided by different laboratories (i.e. up to four orders of magnitude) suggests

that results obtained from different laboratories cannot be compared even on a qualitative

basis. Production simulation modelling is not commonly applied to shale gas plays so having

accurate knowledge of subsurface permeability is probably not a major barrier to shale gas

development. A precise measurement that reflected the gas flow potential of shale may,

however, be useful for identifying producing analogues for shale resource plays undergoing

appraisal. In particular, identification of suitable analogues may provide an early indication

as to whether or not the shale under appraisal is likely to produce at economic rates. The

lack of a standard approach between different laboratories in terms of the experimental

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methodology or calculation of permeability from the pressure transient means that currently it

is not possible to compare results obtained from different laboratories. However, even if

methods were standardized, the crushed shale method would still have the problem that it

does not seem sensitive to the presence of higher permeability streaks that may dominate

flow in the subsurface. The results from the study therefore seem to indicate that the method

is probably totally unsuitable for assessing the permeability of shale on either a quantitative

or comparative basis.

There was, however, reasonable agreement between the laboratories regarding the porosity

values generated using the crushed shale method. This agreement would be even further

improved if a standard procedure was agreed upon to clean the crushed shale. There still,

however, exists the problem of overburden correcting the porosity values. The difficulty in

taking core plugs often means that it is difficult to obtain pore volume compressibilities using

traditional methods. New methods therefore need to be developed to measure pore volume

compressibilities on shale samples with uneven shapes. One possibility would be to use Hg

injection analysis to assess the impact of stress on bulk volume. In particular, Hildenbrand

and Urai (2003) presented evidence that Hg often does not actually enter the pore space of

shale during Hg-injection experiments. If that was the case, the pressure vs injected volume

curves obtained from Hg-injection experiments would in fact represent stress vs

compressibility curves and could therefore be used to estimate the stress dependency of

pore volumes. This clearly requires further work, however, the pore volume multipliers

obtained from Hg injection experiments are very consistent with what would be expected

from shale samples (i.e. 0.75 to 0.95). We are currently working on a technique to coat shale

samples in a thin material that would totally prevent Hg entering pore space during Hg-

injection experiments and then such results could be related to the compressibility of shale

with more certainty.

Conclusions

The crushed shale method has been widely used by industry to measure the porosity and

permeability of shale. Theoretically, the method offers many advantages over traditional

laboratory techniques. The current study has conducted experimental measurements,

numerical modelling and sent six samples to leading service companies for a round-robin

test. The results suggest that the CSM test can provide precise estimates of porosity

measured at ambient stress if standard sample cleaning techniques are used. There are,

however, uncertainties regarding how overburden corrections are made. However, the

results suggest that the CSM does not appear to be useful for measuring permeability in

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either a quantitative or qualitative manner. It would probably be possible to make

measurements more reproducible by adopting standard analytical methods across industry.

However, even with standard workflows, the test may not be particularly useful as a guide to

the flow capacity of shale because it is generally insensitive to the presence of high

permeability streaks that may control subsurface gas flow.

Acknowledgements

We are extremely grateful for the sponsorship of this work provided by Chevron, EBN and

Nexen. Schlumberger and Emerson are thanked for granting us licences to use EclipseTM

and EnableTM.

Nomenclature

b Klinkenberg coefficient (Pa)

DV dead volume (m3)

FR mass fraction of gas

k apparent gas permeability k = k1(1+b⁄P) (m2)

k1 intrinsic permeability (m2, D)

K term defined by � = ΤΥςWΞ(Equation 6)

Kc ratio of the dead volume in the experimental apparatus divided by the pore volume of

the shale

m number of roots used in Equation (7)

P0i initial pressure pulse (Pa)

P0(t) pressure at r = R0 and t (Pa, psig, bar)

P1i initial steady-state pressure (Pa, psig)

Pi pressure in the sample cell after the valve has been opened (Pa, psig)

Pf final steady state pressure (Pa, psig)

Pm mean value of P0 over tf (Pa)

r radial coordinate (m)

R0 particles radius (m)

ST particles total exchange area (m2)

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t time (s)

tD dimensionless time

ti date of measurement (s)

tf duration of the experiment (s)

Vs sample cell volume (m3)

V0 reference cell volume (m3)

V1 crushed sample volume (m3)

Ww weight of wet, crushed rock sample (g)

α1 first root of the equation (11)

βf ideal gas compressibility (Pa-1)

� term defined by Equation (4)

� term defined by Equation (5)

ϕ porosity, fraction

%& roots of Equation (7)

ρb bulk density, g/cm3

ρg grain density, g/cm3

ρc0 initial average gas density in the sample and reference cells

ρr0 initial gas density in the reference cell

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Laboratory characterization of the porosity and permeability of gas

shales using the crushed shale method: Insights from experiments

and numerical modelling

Quentin Fisher, Piroska Lorinczi, Carlos Grattoni, Konstantin Rybalcenko, Anthony J. Crook,

Samuel Allshorn, Alan D. Burns and Ida Shafagh

Highlights

• A round-robin test is reported where 6 shales were analyzed by 4 laboratories.

• Permeabilities measured by each laboratory using the crushed shale method (CSM)

do not correlate.

• Permeabilities vary by orders of magnitude depending on how the data are

interpreted.

• Results from the CSM method do not correlate with measurements made on core

plugs.

• Pressure transient results from CSM experiments were inverted using analytical and

numerical models.